Partial Fraction Decomposition Review for Inverse Laplace Transform.

Write the following fractions as a sum of simpler fractions.

1. (a) \( \displaystyle{\frac{1}{s^2-5s+4} } \)     (b) \( \displaystyle{\frac{s-2}{s^2-2s - 15} } \)     (c) \( \displaystyle{\frac{1}{s^3-9s} } \)   solution

2. (a) \( \displaystyle{\frac{8}{s(s^2+4)} } \)       (b) \( \displaystyle{\frac{4}{(s^2+1)(s^2+9)} } \)   solution